We show that the Matthew effect, or Matthew mechanism, was present in the artificial cultural market Music Lab when social influence between individuals was allowed, whereas this was not the case when social influence was not allowed. We also sketch on a class of social network models, derived from social influence theory, that may generate the Matthew effect. Thus, we propose a theoretical framework that may explain why the most popular songs were much more popular, and the least popular songs were much less popular, than when disallowing social influence between individuals.